Do This by Logic

I thought it was funny that the early reponses decided to show their answers determined by formulas.


They must have skipped over the first sentence in David's post: Again I am trying to get you to think, not blindly use formulas.


They must have missed the point of the exercise. I'll go with 25% too.

If fair coins turn up HH 1/4 of the time that means the other 3/4 of the time it came up HH it would be the double headed coin.


Just a guess since DS asked for logic and not formulas.


Flame away.

4:3= 4/7 = the chances you picked the bad coin

another theory although most likely incorrect.


P(HH for fair coin) = .25

P(HH for unfair) = 1.00


P(unfair HH) divided by P(fair + unfair coins) = .80


1.00/1.25 = 0.80 or 80%


again flame away.

once you flip a coin and get a side, then if you flip it again theres a 50% chance you get the same side in a fair coin, or 100% in a double sided coin.


thats why i say its double fair chance of 1/4.


so 1/2.


but now i see it wasnt a double sided coin but a double headed coin. ugh. too much scotch i guess


brad

(3(.25) + 1(1) )/ 4


=


1.75/4


= 43.75%


?

i think there are two events here


picking


and flicking


(you can easily remember this "formula" by thinking of dynasty's nose)


picking is not affected by flicking


so the chances that you picked the double-headed coin are 1 in 4


once you've picked it it doesn't really matter if you flick ten heads in a row - although unusual, it's already on your finger

We pick the bad coin 1/4 of the time. We get 2 heads 1/4 of the time when we pick the 3 good coins, and all the time when we pick the bad coin, so the total probability that we get 2 heads is (1/4)(3/4) + (1/4)(1) = 7/16. So the fraction of the time we have the bad coin when we get 2 heads is (1/4)/(7/16) = 4/7.